{"title":"Asymptotic dimension of graphs of groups and one-relator groups","authors":"Panagiotis Tselekidis","doi":"10.2140/agt.2023.23.3587","DOIUrl":null,"url":null,"abstract":"We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"37 5","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.3587","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
We prove a new inequality for the asymptotic dimension of HNN-extensions. We deduce that the asymptotic dimension of every one relator group is at most two, confirming a conjecture of A.Dranishnikov. As another corollary we calculate the exact asymptotic dimension of Right-angled Artin groups. We prove a new upper bound for the asymptotic dimension of fundamental groups of graphs of groups. This leads to a partial result on the asymptotic Morita conjecture for finitely generated groups.
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